The White House said Wednesday that it is "crystal clear" that the separatists in eastern Ukraine and Russia are not living up to the cease-fire agreement negotiated last week in Minsk, Belarus, and warned of possible costs.

“We believe that it is important for all sides to live up to [the Minsk] agreement. It is also crystal clear that Russia-backed separatists and Russia themselves have not lived up to their commitments that they made in the context of [the Minsk] negotiations,” spokesman Josh Earnest told reporters.

Earnest added that the separatists and Moscow may incur “greater costs” and “should be mindful of that as they consider their next steps.”

He said that Washington continues to believe that “the way the situation can be revolved is around the negotiating table."

Rebels take Debaltseve

The comments came after separatists took control of Debaltseve, a strategic rail hub that links the separatist-controlled areas in Ukraine’s Donetsk and Luhansk regions.

The rebels hoisted their flag Wednesday in triumph in the town has seen continued fighting since a cease-fire went into effect early Sunday.

Ukrainian President Petro Poroshenko ordered several thousand of Kyiv's troops to leave Debaltseve after rebels reported taking hundreds of government forces captive and left its remaining fighters short of food and water.

Poroshenko said 80 percent of goverment troops had left the city by early Wednesday, and the rest were leaving in what he described as a planned and orderly withdrawal. He later visited the frontlines to meet with returning soldiers.

Map of Debaltseve, Ukraine

Poroshenko said the withdrawal "laid shame on Russia" for its support of the separatists.

Meanwhile, Poroshenko's office reported late Wednesday that his government will ask the United Nations to send a peacekeeping mission to eastern Ukraine. He announced the move during a meeting of the country's National Defense and Security Council.

Putin gloats

Tuesday in Hungary, Russian President Vladimir Putin took a more philosophical view of Kyiv's losing control over Debaltseve and said the cease-fire negotiated last week must be implemented.

"Of course, it is always bad to lose. Of course, it is always painful to lose, especially if you lose to yesterday's miners and tractor mechanics," Putin said, referring to rebel fighters Kyiv and many Western goverments claim are supported by Moscow with manpower and weapons. "But life is life, and it will definitely go on.... We should resolve the main task -- save lives of lives of the people who are there now, to insure that they would return to their families, and fulfill the whole plan agreed on in Minsk,'' said Putin.

Germany condemned on Wednesday the pro-Russian separatists' offensive at Debaltseve, calling it a clear violation of a cease-fire agreed to last week, but said it was too early to call the broader Minsk peace deal dead.

Ukrainian President Petro Poroshenko, right, shakes hands with Ukrainian servicemen in the town of Artemivsk, Ukraine, Feb. 18, 2015.

EU, NATO reaction

Also stepping up Western criticism of the rebel offensive on Debaltseve, European Union foreign policy chief Federica Mogherini said in Brussels, "The actions by the Russia-backed separatists in Debaltseve are a clear violation of the cease-fire.

“The EU stands ready to take appropriate action in case the fighting and other negative developments in violation of the Minsk agreements continue,” she said, making an apparent threat of further economic sanctions on Moscow.

Voicing his concerns about fighting at Debaltseve, NATO Secretary-General Jens Stoltenberg said the refusal of pro-Russian separatists to respect the cease-fire threatened the Minsk accord.

“The refusal of the separatists to respect the cease-fire threatens the agreement, as does their denial of access to the area for the OSCE monitors,” Stoltenberg told reporters in the Latvian capital where he was attending a meeting of European Union defense ministers.

He also said Russian forces, artillery and air defense units were still active in Ukraine.

Tuesday, the U.N. Security Council unanimously adopted a resolution drafted by Russia that supports the Minsk cease-fire deal, while calling for rebels to respect the territorial integrity of Ukraine.

Meanwhile, Ukraine is approaching the first anniversary on February 20 of the Maidan uprising, when months of anti-government protests in Kyiv turned violent, with security forces opening fire on protesters, killing over a hundred of them. The escalation led Ukraine's Moscow-backed president Viktor Yanukovych to flee Kyiv for Russia.